Many-body effects on properties of attractive Bose-Einstein condensates.

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We have studied effects of interactions on properties of gaseous Bose-Einstein condensates (BECs) by focusing on many-body effect and attractive interactions. Below follows the summary of our main results.(1) Fast rotating BEC. We have shown that a rotating BEC makes a quantum phase transition to the Laughlin state when the angular momentum of the system exceeds h N(N-1), where N is the number of atoms. Above the Laughlin state we find a single-particle excitation branch similar to the roton branch. This branch has been found in fractional quantum Hall systems with a long-range Coulomb interaction. Our system has short-ranged and therefore offers a new insight into this gapful mode.(2) A BEC is usually created in a confining potential. It is well known that in dimensions higher than one dimension BEC will either collapse or expand in free space. We have shown that the BEC can be stabilized in 2D free space by oscillating the strength of interactions between attractive and repulsive interactions using a Feshbach resonance.(3) In 3D free space, we have found that BEC cannot be stabilized by the above method, but can be stabilized in the presence of dissipation. This state of matter may be viewed as a self-trapped gaseous superfluid in free space.